KoAT2 Proof Output

Initial Problem

Start: eval_f_start
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆
Temp_Vars: nondef.0, nondef.1, nondef.2, nondef.3
Locations: eval_f_0, eval_f_1, eval_f_2, eval_f_4, eval_f_5, eval_f_7, eval_f_8, eval_f_bb0_in, eval_f_bb1_in, eval_f_bb2_in, eval_f_bb3_in, eval_f_bb4_in, eval_f_bb5_in, eval_f_bb6_in, eval_f_bb7_in, eval_f_start, eval_f_stop
Transitions:
t₃: eval_f_0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆) → eval_f_1(X₀, X₁, X₂, X₃, X₄, nondef.0, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆)
t₅: eval_f_1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆) → eval_f_2(X₀, X₁, X₂, X₃, X₄, X₅, nondef.1, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆)
t₆: eval_f_2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆) → eval_f_bb1_in(X₅, X₁₆, X₆, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆)
t₁₄: eval_f_4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆) → eval_f_5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, nondef.2, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆)
t₁₅: eval_f_5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆) → eval_f_bb1_in(X₈, X₁, X₉, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆)
t₂₂: eval_f_7(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆) → eval_f_8(X₀, X₁, X₂, X₃, X₄, X₅, X₆, nondef.3, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆)
t₂₃: eval_f_8(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆) → eval_f_bb1_in(X₀, X₁₀, X₇, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆)
t₁: eval_f_bb0_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆) → eval_f_0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆)
t₇: eval_f_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆) → eval_f_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆) :|: X₀ ≤ 3 ∧ 1 ≤ X₀ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0
t₈: eval_f_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆) → eval_f_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆) :|: X₀ ≤ 0
t₉: eval_f_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆) → eval_f_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆) :|: 4 ≤ X₀
t₁₀: eval_f_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆) → eval_f_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆) :|: 1+X₂ ≤ 0
t₁₁: eval_f_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆) → eval_f_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆) :|: 1 ≤ X₂
t₁₂: eval_f_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆) → eval_f_4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, 1+X₀, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆)
t₁₆: eval_f_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆) → eval_f_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆) :|: X₂ ≤ 1 ∧ 1 ≤ X₂ ∧ 2 ≤ X₁
t₁₇: eval_f_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆) → eval_f_bb5_in(X₀, X₁, X₂, X₁₁, X₁₂, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆) :|: X₁ ≤ 1
t₁₈: eval_f_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆) → eval_f_bb5_in(X₀, X₁, X₂, X₁₁, X₁₂, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆) :|: X₂ ≤ 0
t₁₉: eval_f_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆) → eval_f_bb5_in(X₀, X₁, X₂, X₁₁, X₁₂, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆) :|: 2 ≤ X₂
t₂₀: eval_f_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆) → eval_f_7(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁-1, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆)
t₂₄: eval_f_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆) → eval_f_bb6_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆) :|: 1 ≤ X₃ ∧ 1+X₃ ≤ (X₄)²
t₂₅: eval_f_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆) → eval_f_bb7_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆) :|: (X₄)² ≤ X₃
t₂₆: eval_f_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆) → eval_f_bb7_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆) :|: X₃ ≤ 0
t₂₇: eval_f_bb6_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆) → eval_f_bb5_in(X₀, X₁, X₂, 5⋅X₃+(X₁₃)², 2⋅X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆)
t₂₈: eval_f_bb7_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆) → eval_f_stop(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆)
t₀: eval_f_start(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆) → eval_f_bb0_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆)

Preprocessing

Eliminate variables [X₁₄; X₁₅] that do not contribute to the problem

Found invariant X₅ ≤ X₀ ∧ X₁ ≤ X₁₄ for location eval_f_bb1_in

Found invariant X₅ ≤ X₀ ∧ X₂ ≤ 1 ∧ 1+X₂ ≤ X₁₄ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 3 ≤ X₂+X₁₄ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₁₄ ∧ 4 ≤ X₁+X₁₄ ∧ X₁ ≤ X₁₄ ∧ 2 ≤ X₁ for location eval_f_bb4_in

Found invariant X₈ ≤ 4 ∧ X₅+X₈ ≤ 7 ∧ X₈ ≤ 4+X₂ ∧ X₂+X₈ ≤ 4 ∧ X₈ ≤ 1+X₀ ∧ X₀+X₈ ≤ 7 ∧ 2 ≤ X₈ ∧ 1+X₅ ≤ X₈ ∧ 2 ≤ X₂+X₈ ∧ 2+X₂ ≤ X₈ ∧ 3 ≤ X₀+X₈ ∧ 1+X₀ ≤ X₈ ∧ X₅ ≤ 3 ∧ X₅ ≤ 3+X₂ ∧ X₂+X₅ ≤ 3 ∧ X₅ ≤ X₀ ∧ X₀+X₅ ≤ 6 ∧ X₂ ≤ 0 ∧ 1+X₂ ≤ X₀ ∧ X₀+X₂ ≤ 3 ∧ 0 ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ X₀ ≤ 3+X₂ ∧ X₁ ≤ X₁₄ ∧ X₀ ≤ 3 ∧ 1 ≤ X₀ for location eval_f_4

Found invariant X₅ ≤ X₀ ∧ X₁₁ ≤ X₃ ∧ X₁ ≤ X₁₄ for location eval_f_bb7_in

Found invariant X₅ ≤ X₀ ∧ X₁₁ ≤ X₃ ∧ X₁ ≤ X₁₄ for location eval_f_bb5_in

Found invariant X₅ ≤ X₀ ∧ X₂ ≤ 1 ∧ 1+X₂ ≤ X₁₄ ∧ X₂ ≤ X₁₀ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 3 ≤ X₂+X₁₄ ∧ 2 ≤ X₂+X₁₀ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₁₄ ∧ 3 ≤ X₁₀+X₁₄ ∧ 1+X₁₀ ≤ X₁₄ ∧ 4 ≤ X₁+X₁₄ ∧ X₁ ≤ X₁₄ ∧ 1+X₁₀ ≤ X₁ ∧ 1 ≤ X₁₀ ∧ 3 ≤ X₁+X₁₀ ∧ X₁ ≤ 1+X₁₀ ∧ 2 ≤ X₁ for location eval_f_8

Found invariant X₅ ≤ X₀ ∧ X₁ ≤ X₁₄ for location eval_f_bb3_in

Found invariant X₅ ≤ X₀ ∧ X₁₁ ≤ X₃ ∧ X₁ ≤ X₁₄ for location eval_f_stop

Found invariant X₅ ≤ 3 ∧ X₅ ≤ 3+X₂ ∧ X₂+X₅ ≤ 3 ∧ X₅ ≤ X₀ ∧ X₀+X₅ ≤ 6 ∧ X₂ ≤ 0 ∧ 1+X₂ ≤ X₀ ∧ X₀+X₂ ≤ 3 ∧ 0 ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ X₀ ≤ 3+X₂ ∧ X₁ ≤ X₁₄ ∧ X₀ ≤ 3 ∧ 1 ≤ X₀ for location eval_f_bb2_in

Found invariant X₅ ≤ X₀ ∧ 1 ≤ X₃ ∧ X₁₁ ≤ X₃ ∧ X₁ ≤ X₁₄ for location eval_f_bb6_in

Problem after Preprocessing

MPRF for transition t₅₉: eval_f_7(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → eval_f_8(X₀, X₁, X₂, X₃, X₄, X₅, X₆, nondef.3, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) :|: X₁ ≤ 1+X₁₀ ∧ X₂ ≤ 1 ∧ 1+X₂ ≤ X₁ ∧ 1+X₁₀ ≤ X₁ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₁₄ ∧ 1 ≤ X₁₀ ∧ 1+X₁₀ ≤ X₁₄ ∧ 2 ≤ X₁ ∧ 2 ≤ X₂+X₁₀ ∧ 2 ≤ X₁₄ ∧ 3 ≤ X₁+X₂ ∧ 3 ≤ X₁+X₁₀ ∧ 3 ≤ X₂+X₁₄ ∧ 3 ≤ X₁₀+X₁₄ ∧ 4 ≤ X₁+X₁₄ ∧ X₅ ≤ X₀ ∧ X₁ ≤ X₁₄ ∧ X₂ ≤ X₁₀ of depth 1:

new bound:

X₁₄+1 {O(n)}

MPRF:

• eval_f_4: [X₁-1]
• eval_f_5: [X₁-1]
• eval_f_7: [X₁-1]
• eval_f_8: [X₁-2]
• eval_f_bb1_in: [X₁-1]
• eval_f_bb2_in: [X₁-1]
• eval_f_bb3_in: [X₁-1]
• eval_f_bb4_in: [X₁-1]

MPRF for transition t₆₀: eval_f_8(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → eval_f_bb1_in(X₀, X₁₀, X₇, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) :|: X₁ ≤ 1+X₁₀ ∧ X₂ ≤ 1 ∧ 1+X₂ ≤ X₁ ∧ 1+X₁₀ ≤ X₁ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₁₄ ∧ 1 ≤ X₁₀ ∧ 1+X₁₀ ≤ X₁₄ ∧ 2 ≤ X₁ ∧ 2 ≤ X₂+X₁₀ ∧ 2 ≤ X₁₄ ∧ 3 ≤ X₁+X₂ ∧ 3 ≤ X₁+X₁₀ ∧ 3 ≤ X₂+X₁₄ ∧ 3 ≤ X₁₀+X₁₄ ∧ 4 ≤ X₁+X₁₄ ∧ X₅ ≤ X₀ ∧ X₁ ≤ X₁₄ ∧ X₂ ≤ X₁₀ of depth 1:

new bound:

X₁₄+1 {O(n)}

MPRF:

• eval_f_4: [X₁-1]
• eval_f_5: [X₁-1]
• eval_f_7: [X₁₀]
• eval_f_8: [X₁₀]
• eval_f_bb1_in: [X₁-1]
• eval_f_bb2_in: [X₁-1]
• eval_f_bb3_in: [X₁-1]
• eval_f_bb4_in: [X₁-1]

MPRF for transition t₆₈: eval_f_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → eval_f_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) :|: X₂ ≤ 1 ∧ 1 ≤ X₂ ∧ 2 ≤ X₁ ∧ X₅ ≤ X₀ ∧ X₁ ≤ X₁₄ of depth 1:

new bound:

X₁₄+1 {O(n)}

MPRF:

• eval_f_4: [1+X₁]
• eval_f_5: [1+X₁]
• eval_f_7: [X₁]
• eval_f_8: [X₁]
• eval_f_bb1_in: [1+X₁]
• eval_f_bb2_in: [1+X₁]
• eval_f_bb3_in: [1+X₁]
• eval_f_bb4_in: [X₁]

MPRF for transition t₇₂: eval_f_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → eval_f_7(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁-1, X₁₁, X₁₂, X₁₃, X₁₄) :|: X₂ ≤ 1 ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₁₄ ∧ 2 ≤ X₁ ∧ 2 ≤ X₁₄ ∧ 3 ≤ X₁+X₂ ∧ 3 ≤ X₂+X₁₄ ∧ 4 ≤ X₁+X₁₄ ∧ X₅ ≤ X₀ ∧ X₁ ≤ X₁₄ of depth 1:

new bound:

X₁₄+1 {O(n)}

MPRF:

• eval_f_4: [X₁-1]
• eval_f_5: [X₁-1]
• eval_f_7: [X₁-2]
• eval_f_8: [X₁-2]
• eval_f_bb1_in: [X₁-1]
• eval_f_bb2_in: [X₁-1]
• eval_f_bb3_in: [X₁-1]
• eval_f_bb4_in: [X₁-1]

knowledge_propagation leads to new time bound X₁₄+2 {O(n)} for transition t₆₃: eval_f_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → eval_f_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) :|: X₀ ≤ 0 ∧ X₅ ≤ X₀ ∧ X₁ ≤ X₁₄

MPRF for transition t₆₄: eval_f_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → eval_f_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) :|: 4 ≤ X₀ ∧ X₅ ≤ X₀ ∧ X₁ ≤ X₁₄ of depth 1:

new bound:

X₁₄+2 {O(n)}

MPRF:

• eval_f_4: [1]
• eval_f_5: [1]
• eval_f_7: [1]
• eval_f_8: [1]
• eval_f_bb1_in: [1]
• eval_f_bb2_in: [1]
• eval_f_bb3_in: [0]
• eval_f_bb4_in: [X₂-1]

MPRF for transition t₆₅: eval_f_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → eval_f_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) :|: 1+X₂ ≤ 0 ∧ X₅ ≤ X₀ ∧ X₁ ≤ X₁₄ of depth 1:

new bound:

X₁₄+2 {O(n)}

MPRF:

• eval_f_4: [1]
• eval_f_5: [1]
• eval_f_7: [1]
• eval_f_8: [1]
• eval_f_bb1_in: [1]
• eval_f_bb2_in: [1]
• eval_f_bb3_in: [0]
• eval_f_bb4_in: [0]

MPRF for transition t₆₆: eval_f_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → eval_f_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) :|: 1 ≤ X₂ ∧ X₅ ≤ X₀ ∧ X₁ ≤ X₁₄ of depth 1:

new bound:

X₁₄+2 {O(n)}

MPRF:

• eval_f_4: [1]
• eval_f_5: [1]
• eval_f_7: [1]
• eval_f_8: [1]
• eval_f_bb1_in: [1]
• eval_f_bb2_in: [1]
• eval_f_bb3_in: [0]
• eval_f_bb4_in: [0]

Found invariant X₅ ≤ 3 ∧ X₅ ≤ 3+X₂ ∧ X₂+X₅ ≤ 3 ∧ X₅ ≤ X₀ ∧ X₀+X₅ ≤ 6 ∧ X₂ ≤ 0 ∧ 1+X₂ ≤ X₀ ∧ X₀+X₂ ≤ 3 ∧ 0 ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ X₀ ≤ 3+X₂ ∧ X₁ ≤ X₁₄ ∧ X₀ ≤ 3 ∧ 1 ≤ X₀ for location eval_f_bb2_in_v1

Found invariant X₅ ≤ X₀ ∧ X₁ ≤ X₁₄ for location eval_f_bb1_in

Found invariant X₉ ≤ 0 ∧ 2+X₉ ≤ X₈ ∧ X₈+X₉ ≤ 3 ∧ X₅+X₉ ≤ 2 ∧ X₉ ≤ X₂ ∧ X₂+X₉ ≤ 0 ∧ 2+X₉ ≤ X₀ ∧ X₀+X₉ ≤ 3 ∧ 0 ≤ X₉ ∧ 2 ≤ X₈+X₉ ∧ X₈ ≤ 3+X₉ ∧ X₅ ≤ 2+X₉ ∧ 0 ≤ X₂+X₉ ∧ X₂ ≤ X₉ ∧ 2 ≤ X₀+X₉ ∧ X₀ ≤ 3+X₉ ∧ X₈ ≤ 3 ∧ X₅+X₈ ≤ 5 ∧ X₈ ≤ 3+X₂ ∧ X₂+X₈ ≤ 3 ∧ X₈ ≤ X₀ ∧ X₀+X₈ ≤ 6 ∧ 2 ≤ X₈ ∧ 1+X₅ ≤ X₈ ∧ 2 ≤ X₂+X₈ ∧ 2+X₂ ≤ X₈ ∧ 4 ≤ X₀+X₈ ∧ X₀ ≤ X₈ ∧ X₅ ≤ 2 ∧ X₅ ≤ 2+X₂ ∧ X₂+X₅ ≤ 2 ∧ 1+X₅ ≤ X₀ ∧ X₀+X₅ ≤ 5 ∧ X₂ ≤ 0 ∧ 2+X₂ ≤ X₀ ∧ X₀+X₂ ≤ 3 ∧ 0 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ 3+X₂ ∧ X₁ ≤ X₁₄ ∧ X₀ ≤ 3 ∧ 2 ≤ X₀ for location eval_f_bb2_in_v2

Found invariant X₅ ≤ X₀ ∧ X₁₁ ≤ X₃ ∧ X₁ ≤ X₁₄ for location eval_f_bb7_in

Found invariant X₅ ≤ X₀ ∧ X₁₁ ≤ X₃ ∧ X₁ ≤ X₁₄ for location eval_f_bb5_in

Found invariant X₈ ≤ 4 ∧ X₅+X₈ ≤ 6 ∧ X₈ ≤ 4+X₂ ∧ X₂+X₈ ≤ 4 ∧ X₈ ≤ 1+X₀ ∧ X₀+X₈ ≤ 7 ∧ 3 ≤ X₈ ∧ 2+X₅ ≤ X₈ ∧ 3 ≤ X₂+X₈ ∧ 3+X₂ ≤ X₈ ∧ 5 ≤ X₀+X₈ ∧ 1+X₀ ≤ X₈ ∧ X₅ ≤ 2 ∧ X₅ ≤ 2+X₂ ∧ X₂+X₅ ≤ 2 ∧ 1+X₅ ≤ X₀ ∧ X₀+X₅ ≤ 5 ∧ X₂ ≤ 0 ∧ 2+X₂ ≤ X₀ ∧ X₀+X₂ ≤ 3 ∧ 0 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ 3+X₂ ∧ X₁ ≤ X₁₄ ∧ X₀ ≤ 3 ∧ 2 ≤ X₀ for location eval_f_5_v2

Found invariant X₅ ≤ X₀ ∧ X₁ ≤ X₁₄ for location eval_f_bb3_in

Found invariant X₉ ≤ X₂ ∧ X₂ ≤ X₉ ∧ X₈ ≤ 4 ∧ X₅+X₈ ≤ 7 ∧ X₈ ≤ X₀ ∧ X₀+X₈ ≤ 8 ∧ 2 ≤ X₈ ∧ 1+X₅ ≤ X₈ ∧ 4 ≤ X₀+X₈ ∧ X₀ ≤ X₈ ∧ X₅ ≤ 3 ∧ 1+X₅ ≤ X₀ ∧ X₀+X₅ ≤ 7 ∧ X₁ ≤ X₁₄ ∧ X₀ ≤ 4 ∧ 2 ≤ X₀ for location eval_f_bb1_in_v1

Found invariant X₅ ≤ X₀ ∧ X₁₁ ≤ X₃ ∧ X₁ ≤ X₁₄ for location eval_f_stop

Found invariant X₉ ≤ 0 ∧ 3+X₉ ≤ X₈ ∧ X₈+X₉ ≤ 4 ∧ X₅+X₉ ≤ 2 ∧ X₉ ≤ X₂ ∧ X₂+X₉ ≤ 0 ∧ 2+X₉ ≤ X₀ ∧ X₀+X₉ ≤ 3 ∧ 0 ≤ X₉ ∧ 3 ≤ X₈+X₉ ∧ X₈ ≤ 4+X₉ ∧ X₅ ≤ 2+X₉ ∧ 0 ≤ X₂+X₉ ∧ X₂ ≤ X₉ ∧ 2 ≤ X₀+X₉ ∧ X₀ ≤ 3+X₉ ∧ X₈ ≤ 4 ∧ X₅+X₈ ≤ 6 ∧ X₈ ≤ 4+X₂ ∧ X₂+X₈ ≤ 4 ∧ X₈ ≤ 1+X₀ ∧ X₀+X₈ ≤ 7 ∧ 3 ≤ X₈ ∧ 2+X₅ ≤ X₈ ∧ 3 ≤ X₂+X₈ ∧ 3+X₂ ≤ X₈ ∧ 5 ≤ X₀+X₈ ∧ 1+X₀ ≤ X₈ ∧ X₅ ≤ 2 ∧ X₅ ≤ 2+X₂ ∧ X₂+X₅ ≤ 2 ∧ 1+X₅ ≤ X₀ ∧ X₀+X₅ ≤ 5 ∧ X₂ ≤ 0 ∧ 2+X₂ ≤ X₀ ∧ X₀+X₂ ≤ 3 ∧ 0 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ 3+X₂ ∧ X₁ ≤ X₁₄ ∧ X₀ ≤ 3 ∧ 2 ≤ X₀ for location eval_f_4_v2

Found invariant X₅ ≤ X₀ ∧ 1 ≤ X₃ ∧ X₁₁ ≤ X₃ ∧ X₁ ≤ X₁₄ for location eval_f_bb6_in

Analysing control-flow refined program

knowledge_propagation leads to new time bound X₁₄+2 {O(n)} for transition t₁₄₅: eval_f_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → eval_f_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) :|: 1 ≤ X₂ ∧ X₅ ≤ X₀ ∧ X₁ ≤ X₁₄

knowledge_propagation leads to new time bound X₁₄+2 {O(n)} for transition t₁₄₆: eval_f_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → eval_f_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) :|: 1+X₂ ≤ 0 ∧ X₅ ≤ X₀ ∧ X₁ ≤ X₁₄

knowledge_propagation leads to new time bound X₁₄+2 {O(n)} for transition t₁₄₇: eval_f_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → eval_f_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) :|: 4 ≤ X₀ ∧ X₅ ≤ X₀ ∧ X₁ ≤ X₁₄

knowledge_propagation leads to new time bound X₁₄+2 {O(n)} for transition t₁₄₈: eval_f_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → eval_f_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) :|: X₀ ≤ 0 ∧ X₅ ≤ X₀ ∧ X₁ ≤ X₁₄

knowledge_propagation leads to new time bound X₁₄+2 {O(n)} for transition t₁₄₉: eval_f_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → eval_f_bb2_in_v1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) :|: X₀ ≤ 3 ∧ 1 ≤ X₀ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0 ∧ X₅ ≤ X₀ ∧ X₁ ≤ X₁₄

knowledge_propagation leads to new time bound X₁₄+2 {O(n)} for transition t₁₅₀: eval_f_bb2_in_v1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → eval_f_4_v1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, 1+X₀, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) :|: X₀+X₅ ≤ 6 ∧ X₀ ≤ 3 ∧ X₀ ≤ 3+X₂ ∧ X₀+X₂ ≤ 3 ∧ X₅ ≤ 3+X₂ ∧ X₂+X₅ ≤ 3 ∧ X₅ ≤ 3 ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₂ ∧ 1+X₂ ≤ X₀ ∧ X₅ ≤ X₀ ∧ X₁ ≤ X₁₄ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0

knowledge_propagation leads to new time bound X₁₄+2 {O(n)} for transition t₁₅₁: eval_f_4_v1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → eval_f_5_v1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, nondef.2, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) :|: X₀+X₈ ≤ 7 ∧ X₅+X₈ ≤ 7 ∧ X₀+X₅ ≤ 6 ∧ X₈ ≤ 4+X₂ ∧ X₂+X₈ ≤ 4 ∧ X₈ ≤ 4 ∧ X₀ ≤ 3 ∧ X₀ ≤ 3+X₂ ∧ X₀+X₂ ≤ 3 ∧ X₅ ≤ 3+X₂ ∧ X₂+X₅ ≤ 3 ∧ X₅ ≤ 3 ∧ X₈ ≤ 1+X₀ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₂ ∧ 1+X₂ ≤ X₀ ∧ 1+X₀ ≤ X₈ ∧ 1+X₅ ≤ X₈ ∧ 2 ≤ X₂+X₈ ∧ 2+X₂ ≤ X₈ ∧ 2 ≤ X₈ ∧ 3 ≤ X₀+X₈ ∧ X₅ ≤ X₀ ∧ X₁ ≤ X₁₄ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0

knowledge_propagation leads to new time bound X₁₄+2 {O(n)} for transition t₁₅₂: eval_f_5_v1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → eval_f_bb1_in_v1(X₈, X₁, X₉, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) :|: X₀+X₈ ≤ 7 ∧ X₅+X₈ ≤ 7 ∧ X₀+X₅ ≤ 6 ∧ X₈ ≤ 4+X₂ ∧ X₂+X₈ ≤ 4 ∧ X₈ ≤ 4 ∧ X₀ ≤ 3 ∧ X₀ ≤ 3+X₂ ∧ X₀+X₂ ≤ 3 ∧ X₅ ≤ 3+X₂ ∧ X₂+X₅ ≤ 3 ∧ X₅ ≤ 3 ∧ X₈ ≤ 1+X₀ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₂ ∧ 1+X₂ ≤ X₀ ∧ 1+X₀ ≤ X₈ ∧ 1+X₅ ≤ X₈ ∧ 2 ≤ X₂+X₈ ∧ 2+X₂ ≤ X₈ ∧ 2 ≤ X₈ ∧ 3 ≤ X₀+X₈ ∧ X₅ ≤ X₀ ∧ X₁ ≤ X₁₄ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0

MPRF for transition t₁₅₃: eval_f_bb1_in_v1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → eval_f_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) :|: 1 ≤ X₂ ∧ X₀+X₈ ≤ 8 ∧ X₀+X₅ ≤ 7 ∧ X₅+X₈ ≤ 7 ∧ X₀ ≤ 4 ∧ X₈ ≤ 4 ∧ X₅ ≤ 3 ∧ 1 ≤ X₀ ∧ 1+X₅ ≤ X₀ ∧ 1+X₅ ≤ X₈ ∧ 2 ≤ X₀ ∧ 2 ≤ X₈ ∧ 4 ≤ X₀+X₈ ∧ X₅ ≤ X₀ ∧ X₈ ≤ X₀ ∧ X₀ ≤ X₈ ∧ X₁ ≤ X₁₄ ∧ X₉ ≤ X₂ ∧ X₂ ≤ X₉ of depth 1:

new bound:

21⋅X₁₄+46 {O(n)}

MPRF:

• eval_f_4_v1: [4]
• eval_f_4_v2: [15-2⋅X₈]
• eval_f_5_v1: [5+X₀-X₈]
• eval_f_5_v2: [7]
• eval_f_7: [4]
• eval_f_8: [4]
• eval_f_bb1_in: [4]
• eval_f_bb1_in_v1: [13-X₀-X₈]
• eval_f_bb2_in_v1: [4]
• eval_f_bb2_in_v2: [13-2⋅X₀]
• eval_f_bb3_in: [4]
• eval_f_bb4_in: [4]

MPRF for transition t₁₅₄: eval_f_bb1_in_v1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → eval_f_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) :|: 1+X₂ ≤ 0 ∧ X₀+X₈ ≤ 8 ∧ X₀+X₅ ≤ 7 ∧ X₅+X₈ ≤ 7 ∧ X₀ ≤ 4 ∧ X₈ ≤ 4 ∧ X₅ ≤ 3 ∧ 1 ≤ X₀ ∧ 1+X₅ ≤ X₀ ∧ 1+X₅ ≤ X₈ ∧ 2 ≤ X₀ ∧ 2 ≤ X₈ ∧ 4 ≤ X₀+X₈ ∧ X₅ ≤ X₀ ∧ X₈ ≤ X₀ ∧ X₀ ≤ X₈ ∧ X₁ ≤ X₁₄ ∧ X₉ ≤ X₂ ∧ X₂ ≤ X₉ of depth 1:

new bound:

5⋅X₁₄+14 {O(n)}

MPRF:

• eval_f_4_v1: [5+X₀-X₈]
• eval_f_4_v2: [5]
• eval_f_5_v1: [5+X₀-X₈]
• eval_f_5_v2: [4+X₈-X₀]
• eval_f_7: [4⋅X₁+4⋅X₂-4-4⋅X₁₀]
• eval_f_8: [4⋅X₁-4⋅X₁₀]
• eval_f_bb1_in: [4]
• eval_f_bb1_in_v1: [5]
• eval_f_bb2_in_v1: [4]
• eval_f_bb2_in_v2: [5]
• eval_f_bb3_in: [4]
• eval_f_bb4_in: [4⋅X₂]

MPRF for transition t₁₅₅: eval_f_bb1_in_v1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → eval_f_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) :|: 4 ≤ X₀ ∧ X₀+X₈ ≤ 8 ∧ X₀+X₅ ≤ 7 ∧ X₅+X₈ ≤ 7 ∧ X₀ ≤ 4 ∧ X₈ ≤ 4 ∧ X₅ ≤ 3 ∧ 1 ≤ X₀ ∧ 1+X₅ ≤ X₀ ∧ 1+X₅ ≤ X₈ ∧ 2 ≤ X₀ ∧ 2 ≤ X₈ ∧ 4 ≤ X₀+X₈ ∧ X₅ ≤ X₀ ∧ X₈ ≤ X₀ ∧ X₀ ≤ X₈ ∧ X₁ ≤ X₁₄ ∧ X₉ ≤ X₂ ∧ X₂ ≤ X₉ of depth 1:

new bound:

13⋅X₁₄+30 {O(n)}

MPRF:

• eval_f_4_v1: [4]
• eval_f_4_v2: [8⋅X₈-9⋅X₀]
• eval_f_5_v1: [4]
• eval_f_5_v2: [8⋅X₈-9⋅X₀]
• eval_f_7: [4]
• eval_f_8: [4⋅X₂]
• eval_f_bb1_in: [4]
• eval_f_bb1_in_v1: [9-X₀]
• eval_f_bb2_in_v1: [4]
• eval_f_bb2_in_v2: [9-X₀]
• eval_f_bb3_in: [4]
• eval_f_bb4_in: [4⋅X₂]

MPRF for transition t₁₅₆: eval_f_bb1_in_v1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → eval_f_bb2_in_v2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) :|: X₀ ≤ 3 ∧ 1 ≤ X₀ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0 ∧ X₀+X₈ ≤ 8 ∧ X₀+X₅ ≤ 7 ∧ X₅+X₈ ≤ 7 ∧ X₀ ≤ 4 ∧ X₈ ≤ 4 ∧ X₅ ≤ 3 ∧ 1+X₅ ≤ X₀ ∧ 1+X₅ ≤ X₈ ∧ 2 ≤ X₀ ∧ 2 ≤ X₈ ∧ 4 ≤ X₀+X₈ ∧ X₅ ≤ X₀ ∧ X₈ ≤ X₀ ∧ X₀ ≤ X₈ ∧ X₁ ≤ X₁₄ ∧ X₉ ≤ X₂ ∧ X₂ ≤ X₉ of depth 1:

new bound:

12⋅X₁₄+28 {O(n)}

MPRF:

• eval_f_4_v1: [4]
• eval_f_4_v2: [7-X₀]
• eval_f_5_v1: [3]
• eval_f_5_v2: [3+4⋅X₈-5⋅X₀]
• eval_f_7: [4]
• eval_f_8: [4]
• eval_f_bb1_in: [4]
• eval_f_bb1_in_v1: [8-X₀]
• eval_f_bb2_in_v1: [4]
• eval_f_bb2_in_v2: [7-X₀]
• eval_f_bb3_in: [4]
• eval_f_bb4_in: [4]

MPRF for transition t₁₅₇: eval_f_bb2_in_v2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → eval_f_4_v2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, 1+X₀, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) :|: X₀+X₅ ≤ 6 ∧ X₀+X₈ ≤ 6 ∧ X₀+X₅ ≤ 5 ∧ X₅+X₈ ≤ 5 ∧ X₀ ≤ 3 ∧ X₀ ≤ 3+X₂ ∧ X₀+X₂ ≤ 3 ∧ X₀ ≤ 3+X₉ ∧ X₀+X₉ ≤ 3 ∧ X₅ ≤ 3+X₂ ∧ X₈ ≤ 3+X₂ ∧ X₂+X₅ ≤ 3 ∧ X₂+X₈ ≤ 3 ∧ X₅ ≤ 3 ∧ X₈ ≤ 3 ∧ X₈ ≤ 3+X₉ ∧ X₈+X₉ ≤ 3 ∧ X₅ ≤ 2+X₂ ∧ X₂+X₅ ≤ 2 ∧ X₅ ≤ 2 ∧ X₅ ≤ 2+X₉ ∧ X₅+X₉ ≤ 2 ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₂ ∧ 1+X₂ ≤ X₀ ∧ 1+X₅ ≤ X₀ ∧ 1+X₅ ≤ X₈ ∧ 2 ≤ X₀ ∧ 2 ≤ X₀+X₂ ∧ 2+X₂ ≤ X₀ ∧ 2 ≤ X₀+X₉ ∧ 2+X₉ ≤ X₀ ∧ 2 ≤ X₂+X₈ ∧ 2+X₂ ≤ X₈ ∧ 2 ≤ X₈ ∧ 2 ≤ X₈+X₉ ∧ 2+X₉ ≤ X₈ ∧ 4 ≤ X₀+X₈ ∧ X₅ ≤ X₀ ∧ X₈ ≤ X₀ ∧ X₀ ≤ X₈ ∧ X₁ ≤ X₁₄ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₉ ∧ X₉ ≤ X₂ ∧ X₂ ≤ 0 ∧ X₂ ≤ X₉ ∧ X₂+X₉ ≤ 0 ∧ 0 ≤ X₉ ∧ X₉ ≤ 0 of depth 1:

new bound:

19⋅X₁₄+41 {O(n)}

MPRF:

• eval_f_4_v1: [3]
• eval_f_4_v2: [10-2⋅X₀]
• eval_f_5_v1: [3]
• eval_f_5_v2: [9-2⋅X₀]
• eval_f_7: [3]
• eval_f_8: [3]
• eval_f_bb1_in: [3]
• eval_f_bb1_in_v1: [11-2⋅X₈]
• eval_f_bb2_in_v1: [3]
• eval_f_bb2_in_v2: [11-2⋅X₈]
• eval_f_bb3_in: [3]
• eval_f_bb4_in: [3]

MPRF for transition t₁₅₈: eval_f_4_v2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → eval_f_5_v2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, nondef.2, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) :|: X₀+X₈ ≤ 7 ∧ X₅+X₈ ≤ 7 ∧ X₀+X₅ ≤ 6 ∧ X₅+X₈ ≤ 6 ∧ X₀+X₅ ≤ 5 ∧ X₈ ≤ 4+X₂ ∧ X₂+X₈ ≤ 4 ∧ X₈ ≤ 4 ∧ X₈ ≤ 4+X₉ ∧ X₈+X₉ ≤ 4 ∧ X₀ ≤ 3 ∧ X₀ ≤ 3+X₂ ∧ X₀+X₂ ≤ 3 ∧ X₀ ≤ 3+X₉ ∧ X₀+X₉ ≤ 3 ∧ X₅ ≤ 3+X₂ ∧ X₂+X₅ ≤ 3 ∧ X₅ ≤ 3 ∧ X₅ ≤ 2+X₂ ∧ X₂+X₅ ≤ 2 ∧ X₅ ≤ 2 ∧ X₅ ≤ 2+X₉ ∧ X₅+X₉ ≤ 2 ∧ X₈ ≤ 1+X₀ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₂ ∧ 1+X₂ ≤ X₀ ∧ 1+X₅ ≤ X₀ ∧ 1+X₀ ≤ X₈ ∧ 1+X₅ ≤ X₈ ∧ 2 ≤ X₀ ∧ 2 ≤ X₀+X₂ ∧ 2+X₂ ≤ X₀ ∧ 2 ≤ X₀+X₉ ∧ 2+X₉ ≤ X₀ ∧ 2 ≤ X₂+X₈ ∧ 2+X₂ ≤ X₈ ∧ 2+X₅ ≤ X₈ ∧ 2 ≤ X₈ ∧ 3 ≤ X₀+X₈ ∧ 3 ≤ X₂+X₈ ∧ 3+X₂ ≤ X₈ ∧ 3 ≤ X₈ ∧ 3 ≤ X₈+X₉ ∧ 3+X₉ ≤ X₈ ∧ 5 ≤ X₀+X₈ ∧ X₅ ≤ X₀ ∧ X₁ ≤ X₁₄ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₉ ∧ X₉ ≤ X₂ ∧ X₂ ≤ 0 ∧ X₂ ≤ X₉ ∧ X₂+X₉ ≤ 0 ∧ 0 ≤ X₉ ∧ X₉ ≤ 0 of depth 1:

new bound:

94⋅X₁₄+210 {O(n)}

MPRF:

• eval_f_4_v1: [22]
• eval_f_4_v2: [47-5⋅X₈]
• eval_f_5_v1: [22]
• eval_f_5_v2: [46-5⋅X₈]
• eval_f_7: [22]
• eval_f_8: [22]
• eval_f_bb1_in: [22]
• eval_f_bb1_in_v1: [58-7⋅X₀-2⋅X₈]
• eval_f_bb2_in_v1: [22]
• eval_f_bb2_in_v2: [42-5⋅X₀]
• eval_f_bb3_in: [22]
• eval_f_bb4_in: [22]

MPRF for transition t₁₅₉: eval_f_5_v2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → eval_f_bb1_in_v1(X₈, X₁, X₉, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) :|: X₀+X₈ ≤ 7 ∧ X₅+X₈ ≤ 7 ∧ X₀+X₅ ≤ 6 ∧ X₅+X₈ ≤ 6 ∧ X₀+X₅ ≤ 5 ∧ X₈ ≤ 4+X₂ ∧ X₂+X₈ ≤ 4 ∧ X₈ ≤ 4 ∧ X₀ ≤ 3 ∧ X₀ ≤ 3+X₂ ∧ X₀+X₂ ≤ 3 ∧ X₅ ≤ 3+X₂ ∧ X₂+X₅ ≤ 3 ∧ X₅ ≤ 3 ∧ X₅ ≤ 2+X₂ ∧ X₂+X₅ ≤ 2 ∧ X₅ ≤ 2 ∧ X₈ ≤ 1+X₀ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₂ ∧ 1+X₂ ≤ X₀ ∧ 1+X₅ ≤ X₀ ∧ 1+X₀ ≤ X₈ ∧ 1+X₅ ≤ X₈ ∧ 2 ≤ X₀ ∧ 2 ≤ X₀+X₂ ∧ 2+X₂ ≤ X₀ ∧ 2 ≤ X₂+X₈ ∧ 2+X₂ ≤ X₈ ∧ 2+X₅ ≤ X₈ ∧ 2 ≤ X₈ ∧ 3 ≤ X₀+X₈ ∧ 3 ≤ X₂+X₈ ∧ 3+X₂ ≤ X₈ ∧ 3 ≤ X₈ ∧ 5 ≤ X₀+X₈ ∧ X₅ ≤ X₀ ∧ X₁ ≤ X₁₄ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0 of depth 1:

new bound:

36⋅X₁₄+84 {O(n)}

MPRF:

• eval_f_4_v1: [11+X₂+4⋅X₅-X₀-2⋅X₈]
• eval_f_4_v2: [33-5⋅X₈]
• eval_f_5_v1: [11+4⋅X₅-X₀-2⋅X₈]
• eval_f_5_v2: [25-3⋅X₈]
• eval_f_7: [12]
• eval_f_8: [12]
• eval_f_bb1_in: [12]
• eval_f_bb1_in_v1: [24-3⋅X₈]
• eval_f_bb2_in_v1: [12+4⋅X₅-4⋅X₀]
• eval_f_bb2_in_v2: [24-3⋅X₀]
• eval_f_bb3_in: [12]
• eval_f_bb4_in: [12]

CFR: Improvement to new bound with the following program:

method: PartialEvaluation new bound:

O(n)

cfr-program:

Start: eval_f_start
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄
Temp_Vars: nondef.0, nondef.1, nondef.2, nondef.3
Locations: eval_f_0, eval_f_1, eval_f_2, eval_f_4_v1, eval_f_4_v2, eval_f_5_v1, eval_f_5_v2, eval_f_7, eval_f_8, eval_f_bb0_in, eval_f_bb1_in, eval_f_bb1_in_v1, eval_f_bb2_in_v1, eval_f_bb2_in_v2, eval_f_bb3_in, eval_f_bb4_in, eval_f_bb5_in, eval_f_bb6_in, eval_f_bb7_in, eval_f_start, eval_f_stop
Transitions:
t₅₄: eval_f_0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → eval_f_1(X₀, X₁, X₂, X₃, X₄, nondef.0, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄)
t₅₅: eval_f_1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → eval_f_2(X₀, X₁, X₂, X₃, X₄, X₅, nondef.1, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄)
t₅₆: eval_f_2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → eval_f_bb1_in(X₅, X₁₄, X₆, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄)
t₁₅₁: eval_f_4_v1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → eval_f_5_v1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, nondef.2, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) :|: X₀+X₈ ≤ 7 ∧ X₅+X₈ ≤ 7 ∧ X₀+X₅ ≤ 6 ∧ X₈ ≤ 4+X₂ ∧ X₂+X₈ ≤ 4 ∧ X₈ ≤ 4 ∧ X₀ ≤ 3 ∧ X₀ ≤ 3+X₂ ∧ X₀+X₂ ≤ 3 ∧ X₅ ≤ 3+X₂ ∧ X₂+X₅ ≤ 3 ∧ X₅ ≤ 3 ∧ X₈ ≤ 1+X₀ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₂ ∧ 1+X₂ ≤ X₀ ∧ 1+X₀ ≤ X₈ ∧ 1+X₅ ≤ X₈ ∧ 2 ≤ X₂+X₈ ∧ 2+X₂ ≤ X₈ ∧ 2 ≤ X₈ ∧ 3 ≤ X₀+X₈ ∧ X₅ ≤ X₀ ∧ X₁ ≤ X₁₄ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0
t₁₅₈: eval_f_4_v2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → eval_f_5_v2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, nondef.2, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) :|: X₀+X₈ ≤ 7 ∧ X₅+X₈ ≤ 7 ∧ X₀+X₅ ≤ 6 ∧ X₅+X₈ ≤ 6 ∧ X₀+X₅ ≤ 5 ∧ X₈ ≤ 4+X₂ ∧ X₂+X₈ ≤ 4 ∧ X₈ ≤ 4 ∧ X₈ ≤ 4+X₉ ∧ X₈+X₉ ≤ 4 ∧ X₀ ≤ 3 ∧ X₀ ≤ 3+X₂ ∧ X₀+X₂ ≤ 3 ∧ X₀ ≤ 3+X₉ ∧ X₀+X₉ ≤ 3 ∧ X₅ ≤ 3+X₂ ∧ X₂+X₅ ≤ 3 ∧ X₅ ≤ 3 ∧ X₅ ≤ 2+X₂ ∧ X₂+X₅ ≤ 2 ∧ X₅ ≤ 2 ∧ X₅ ≤ 2+X₉ ∧ X₅+X₉ ≤ 2 ∧ X₈ ≤ 1+X₀ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₂ ∧ 1+X₂ ≤ X₀ ∧ 1+X₅ ≤ X₀ ∧ 1+X₀ ≤ X₈ ∧ 1+X₅ ≤ X₈ ∧ 2 ≤ X₀ ∧ 2 ≤ X₀+X₂ ∧ 2+X₂ ≤ X₀ ∧ 2 ≤ X₀+X₉ ∧ 2+X₉ ≤ X₀ ∧ 2 ≤ X₂+X₈ ∧ 2+X₂ ≤ X₈ ∧ 2+X₅ ≤ X₈ ∧ 2 ≤ X₈ ∧ 3 ≤ X₀+X₈ ∧ 3 ≤ X₂+X₈ ∧ 3+X₂ ≤ X₈ ∧ 3 ≤ X₈ ∧ 3 ≤ X₈+X₉ ∧ 3+X₉ ≤ X₈ ∧ 5 ≤ X₀+X₈ ∧ X₅ ≤ X₀ ∧ X₁ ≤ X₁₄ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₉ ∧ X₉ ≤ X₂ ∧ X₂ ≤ 0 ∧ X₂ ≤ X₉ ∧ X₂+X₉ ≤ 0 ∧ 0 ≤ X₉ ∧ X₉ ≤ 0
t₁₅₂: eval_f_5_v1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → eval_f_bb1_in_v1(X₈, X₁, X₉, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) :|: X₀+X₈ ≤ 7 ∧ X₅+X₈ ≤ 7 ∧ X₀+X₅ ≤ 6 ∧ X₈ ≤ 4+X₂ ∧ X₂+X₈ ≤ 4 ∧ X₈ ≤ 4 ∧ X₀ ≤ 3 ∧ X₀ ≤ 3+X₂ ∧ X₀+X₂ ≤ 3 ∧ X₅ ≤ 3+X₂ ∧ X₂+X₅ ≤ 3 ∧ X₅ ≤ 3 ∧ X₈ ≤ 1+X₀ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₂ ∧ 1+X₂ ≤ X₀ ∧ 1+X₀ ≤ X₈ ∧ 1+X₅ ≤ X₈ ∧ 2 ≤ X₂+X₈ ∧ 2+X₂ ≤ X₈ ∧ 2 ≤ X₈ ∧ 3 ≤ X₀+X₈ ∧ X₅ ≤ X₀ ∧ X₁ ≤ X₁₄ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0
t₁₅₉: eval_f_5_v2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → eval_f_bb1_in_v1(X₈, X₁, X₉, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) :|: X₀+X₈ ≤ 7 ∧ X₅+X₈ ≤ 7 ∧ X₀+X₅ ≤ 6 ∧ X₅+X₈ ≤ 6 ∧ X₀+X₅ ≤ 5 ∧ X₈ ≤ 4+X₂ ∧ X₂+X₈ ≤ 4 ∧ X₈ ≤ 4 ∧ X₀ ≤ 3 ∧ X₀ ≤ 3+X₂ ∧ X₀+X₂ ≤ 3 ∧ X₅ ≤ 3+X₂ ∧ X₂+X₅ ≤ 3 ∧ X₅ ≤ 3 ∧ X₅ ≤ 2+X₂ ∧ X₂+X₅ ≤ 2 ∧ X₅ ≤ 2 ∧ X₈ ≤ 1+X₀ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₂ ∧ 1+X₂ ≤ X₀ ∧ 1+X₅ ≤ X₀ ∧ 1+X₀ ≤ X₈ ∧ 1+X₅ ≤ X₈ ∧ 2 ≤ X₀ ∧ 2 ≤ X₀+X₂ ∧ 2+X₂ ≤ X₀ ∧ 2 ≤ X₂+X₈ ∧ 2+X₂ ≤ X₈ ∧ 2+X₅ ≤ X₈ ∧ 2 ≤ X₈ ∧ 3 ≤ X₀+X₈ ∧ 3 ≤ X₂+X₈ ∧ 3+X₂ ≤ X₈ ∧ 3 ≤ X₈ ∧ 5 ≤ X₀+X₈ ∧ X₅ ≤ X₀ ∧ X₁ ≤ X₁₄ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0
t₅₉: eval_f_7(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → eval_f_8(X₀, X₁, X₂, X₃, X₄, X₅, X₆, nondef.3, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) :|: X₁ ≤ 1+X₁₀ ∧ X₂ ≤ 1 ∧ 1+X₂ ≤ X₁ ∧ 1+X₁₀ ≤ X₁ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₁₄ ∧ 1 ≤ X₁₀ ∧ 1+X₁₀ ≤ X₁₄ ∧ 2 ≤ X₁ ∧ 2 ≤ X₂+X₁₀ ∧ 2 ≤ X₁₄ ∧ 3 ≤ X₁+X₂ ∧ 3 ≤ X₁+X₁₀ ∧ 3 ≤ X₂+X₁₄ ∧ 3 ≤ X₁₀+X₁₄ ∧ 4 ≤ X₁+X₁₄ ∧ X₅ ≤ X₀ ∧ X₁ ≤ X₁₄ ∧ X₂ ≤ X₁₀
t₆₀: eval_f_8(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → eval_f_bb1_in(X₀, X₁₀, X₇, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) :|: X₁ ≤ 1+X₁₀ ∧ X₂ ≤ 1 ∧ 1+X₂ ≤ X₁ ∧ 1+X₁₀ ≤ X₁ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₁₄ ∧ 1 ≤ X₁₀ ∧ 1+X₁₀ ≤ X₁₄ ∧ 2 ≤ X₁ ∧ 2 ≤ X₂+X₁₀ ∧ 2 ≤ X₁₄ ∧ 3 ≤ X₁+X₂ ∧ 3 ≤ X₁+X₁₀ ∧ 3 ≤ X₂+X₁₄ ∧ 3 ≤ X₁₀+X₁₄ ∧ 4 ≤ X₁+X₁₄ ∧ X₅ ≤ X₀ ∧ X₁ ≤ X₁₄ ∧ X₂ ≤ X₁₀
t₆₁: eval_f_bb0_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → eval_f_0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄)
t₁₄₉: eval_f_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → eval_f_bb2_in_v1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) :|: X₀ ≤ 3 ∧ 1 ≤ X₀ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0 ∧ X₅ ≤ X₀ ∧ X₁ ≤ X₁₄
t₆₃: eval_f_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → eval_f_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) :|: X₀ ≤ 0 ∧ X₅ ≤ X₀ ∧ X₁ ≤ X₁₄
t₆₄: eval_f_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → eval_f_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) :|: 4 ≤ X₀ ∧ X₅ ≤ X₀ ∧ X₁ ≤ X₁₄
t₆₅: eval_f_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → eval_f_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) :|: 1+X₂ ≤ 0 ∧ X₅ ≤ X₀ ∧ X₁ ≤ X₁₄
t₆₆: eval_f_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → eval_f_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) :|: 1 ≤ X₂ ∧ X₅ ≤ X₀ ∧ X₁ ≤ X₁₄
t₁₄₅: eval_f_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → eval_f_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) :|: 1 ≤ X₂ ∧ X₅ ≤ X₀ ∧ X₁ ≤ X₁₄
t₁₄₆: eval_f_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → eval_f_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) :|: 1+X₂ ≤ 0 ∧ X₅ ≤ X₀ ∧ X₁ ≤ X₁₄
t₁₄₇: eval_f_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → eval_f_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) :|: 4 ≤ X₀ ∧ X₅ ≤ X₀ ∧ X₁ ≤ X₁₄
t₁₄₈: eval_f_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → eval_f_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) :|: X₀ ≤ 0 ∧ X₅ ≤ X₀ ∧ X₁ ≤ X₁₄
t₁₅₆: eval_f_bb1_in_v1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → eval_f_bb2_in_v2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) :|: X₀ ≤ 3 ∧ 1 ≤ X₀ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0 ∧ X₀+X₈ ≤ 8 ∧ X₀+X₅ ≤ 7 ∧ X₅+X₈ ≤ 7 ∧ X₀ ≤ 4 ∧ X₈ ≤ 4 ∧ X₅ ≤ 3 ∧ 1+X₅ ≤ X₀ ∧ 1+X₅ ≤ X₈ ∧ 2 ≤ X₀ ∧ 2 ≤ X₈ ∧ 4 ≤ X₀+X₈ ∧ X₅ ≤ X₀ ∧ X₈ ≤ X₀ ∧ X₀ ≤ X₈ ∧ X₁ ≤ X₁₄ ∧ X₉ ≤ X₂ ∧ X₂ ≤ X₉
t₁₅₃: eval_f_bb1_in_v1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → eval_f_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) :|: 1 ≤ X₂ ∧ X₀+X₈ ≤ 8 ∧ X₀+X₅ ≤ 7 ∧ X₅+X₈ ≤ 7 ∧ X₀ ≤ 4 ∧ X₈ ≤ 4 ∧ X₅ ≤ 3 ∧ 1 ≤ X₀ ∧ 1+X₅ ≤ X₀ ∧ 1+X₅ ≤ X₈ ∧ 2 ≤ X₀ ∧ 2 ≤ X₈ ∧ 4 ≤ X₀+X₈ ∧ X₅ ≤ X₀ ∧ X₈ ≤ X₀ ∧ X₀ ≤ X₈ ∧ X₁ ≤ X₁₄ ∧ X₉ ≤ X₂ ∧ X₂ ≤ X₉
t₁₅₄: eval_f_bb1_in_v1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → eval_f_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) :|: 1+X₂ ≤ 0 ∧ X₀+X₈ ≤ 8 ∧ X₀+X₅ ≤ 7 ∧ X₅+X₈ ≤ 7 ∧ X₀ ≤ 4 ∧ X₈ ≤ 4 ∧ X₅ ≤ 3 ∧ 1 ≤ X₀ ∧ 1+X₅ ≤ X₀ ∧ 1+X₅ ≤ X₈ ∧ 2 ≤ X₀ ∧ 2 ≤ X₈ ∧ 4 ≤ X₀+X₈ ∧ X₅ ≤ X₀ ∧ X₈ ≤ X₀ ∧ X₀ ≤ X₈ ∧ X₁ ≤ X₁₄ ∧ X₉ ≤ X₂ ∧ X₂ ≤ X₉
t₁₅₅: eval_f_bb1_in_v1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → eval_f_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) :|: 4 ≤ X₀ ∧ X₀+X₈ ≤ 8 ∧ X₀+X₅ ≤ 7 ∧ X₅+X₈ ≤ 7 ∧ X₀ ≤ 4 ∧ X₈ ≤ 4 ∧ X₅ ≤ 3 ∧ 1 ≤ X₀ ∧ 1+X₅ ≤ X₀ ∧ 1+X₅ ≤ X₈ ∧ 2 ≤ X₀ ∧ 2 ≤ X₈ ∧ 4 ≤ X₀+X₈ ∧ X₅ ≤ X₀ ∧ X₈ ≤ X₀ ∧ X₀ ≤ X₈ ∧ X₁ ≤ X₁₄ ∧ X₉ ≤ X₂ ∧ X₂ ≤ X₉
t₁₅₀: eval_f_bb2_in_v1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → eval_f_4_v1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, 1+X₀, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) :|: X₀+X₅ ≤ 6 ∧ X₀ ≤ 3 ∧ X₀ ≤ 3+X₂ ∧ X₀+X₂ ≤ 3 ∧ X₅ ≤ 3+X₂ ∧ X₂+X₅ ≤ 3 ∧ X₅ ≤ 3 ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₂ ∧ 1+X₂ ≤ X₀ ∧ X₅ ≤ X₀ ∧ X₁ ≤ X₁₄ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0
t₁₅₇: eval_f_bb2_in_v2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → eval_f_4_v2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, 1+X₀, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) :|: X₀+X₅ ≤ 6 ∧ X₀+X₈ ≤ 6 ∧ X₀+X₅ ≤ 5 ∧ X₅+X₈ ≤ 5 ∧ X₀ ≤ 3 ∧ X₀ ≤ 3+X₂ ∧ X₀+X₂ ≤ 3 ∧ X₀ ≤ 3+X₉ ∧ X₀+X₉ ≤ 3 ∧ X₅ ≤ 3+X₂ ∧ X₈ ≤ 3+X₂ ∧ X₂+X₅ ≤ 3 ∧ X₂+X₈ ≤ 3 ∧ X₅ ≤ 3 ∧ X₈ ≤ 3 ∧ X₈ ≤ 3+X₉ ∧ X₈+X₉ ≤ 3 ∧ X₅ ≤ 2+X₂ ∧ X₂+X₅ ≤ 2 ∧ X₅ ≤ 2 ∧ X₅ ≤ 2+X₉ ∧ X₅+X₉ ≤ 2 ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₂ ∧ 1+X₂ ≤ X₀ ∧ 1+X₅ ≤ X₀ ∧ 1+X₅ ≤ X₈ ∧ 2 ≤ X₀ ∧ 2 ≤ X₀+X₂ ∧ 2+X₂ ≤ X₀ ∧ 2 ≤ X₀+X₉ ∧ 2+X₉ ≤ X₀ ∧ 2 ≤ X₂+X₈ ∧ 2+X₂ ≤ X₈ ∧ 2 ≤ X₈ ∧ 2 ≤ X₈+X₉ ∧ 2+X₉ ≤ X₈ ∧ 4 ≤ X₀+X₈ ∧ X₅ ≤ X₀ ∧ X₈ ≤ X₀ ∧ X₀ ≤ X₈ ∧ X₁ ≤ X₁₄ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₉ ∧ X₉ ≤ X₂ ∧ X₂ ≤ 0 ∧ X₂ ≤ X₉ ∧ X₂+X₉ ≤ 0 ∧ 0 ≤ X₉ ∧ X₉ ≤ 0
t₆₈: eval_f_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → eval_f_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) :|: X₂ ≤ 1 ∧ 1 ≤ X₂ ∧ 2 ≤ X₁ ∧ X₅ ≤ X₀ ∧ X₁ ≤ X₁₄
t₆₉: eval_f_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → eval_f_bb5_in(X₀, X₁, X₂, X₁₁, X₁₂, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) :|: X₁ ≤ 1 ∧ X₅ ≤ X₀ ∧ X₁ ≤ X₁₄
t₇₀: eval_f_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → eval_f_bb5_in(X₀, X₁, X₂, X₁₁, X₁₂, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) :|: X₂ ≤ 0 ∧ X₅ ≤ X₀ ∧ X₁ ≤ X₁₄
t₇₁: eval_f_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → eval_f_bb5_in(X₀, X₁, X₂, X₁₁, X₁₂, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) :|: 2 ≤ X₂ ∧ X₅ ≤ X₀ ∧ X₁ ≤ X₁₄
t₇₂: eval_f_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → eval_f_7(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁-1, X₁₁, X₁₂, X₁₃, X₁₄) :|: X₂ ≤ 1 ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₁₄ ∧ 2 ≤ X₁ ∧ 2 ≤ X₁₄ ∧ 3 ≤ X₁+X₂ ∧ 3 ≤ X₂+X₁₄ ∧ 4 ≤ X₁+X₁₄ ∧ X₅ ≤ X₀ ∧ X₁ ≤ X₁₄
t₇₃: eval_f_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → eval_f_bb6_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) :|: 1 ≤ X₃ ∧ 1+X₃ ≤ (X₄)² ∧ X₅ ≤ X₀ ∧ X₁ ≤ X₁₄ ∧ X₁₁ ≤ X₃
t₇₄: eval_f_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → eval_f_bb7_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) :|: (X₄)² ≤ X₃ ∧ X₅ ≤ X₀ ∧ X₁ ≤ X₁₄ ∧ X₁₁ ≤ X₃
t₇₅: eval_f_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → eval_f_bb7_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) :|: X₃ ≤ 0 ∧ X₅ ≤ X₀ ∧ X₁ ≤ X₁₄ ∧ X₁₁ ≤ X₃
t₇₆: eval_f_bb6_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → eval_f_bb5_in(X₀, X₁, X₂, 5⋅X₃+(X₁₃)², 2⋅X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) :|: 1 ≤ X₃ ∧ X₅ ≤ X₀ ∧ X₁ ≤ X₁₄ ∧ X₁₁ ≤ X₃
t₇₇: eval_f_bb7_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → eval_f_stop(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) :|: X₅ ≤ X₀ ∧ X₁ ≤ X₁₄ ∧ X₁₁ ≤ X₃
t₇₈: eval_f_start(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → eval_f_bb0_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄)

Found invariant X₅ ≤ X₀ ∧ X₁ ≤ X₁₄ for location eval_f_bb1_in

Found invariant X₅ ≤ X₀ ∧ X₁₁ ≤ X₃ ∧ X₁ ≤ X₁₄ for location eval_f_bb7_in

Found invariant X₅ ≤ X₀ ∧ X₄ ≤ X₁₂ ∧ X₁₂ ≤ X₄ ∧ X₃ ≤ X₁₁ ∧ X₁₁ ≤ X₃ ∧ X₁ ≤ X₁₄ for location eval_f_bb5_in

Found invariant X₅ ≤ X₀ ∧ 1 ≤ X₃ ∧ 2 ≤ X₃+X₁₁ ∧ X₁₁ ≤ X₃ ∧ X₁ ≤ X₁₄ ∧ 1 ≤ X₁₁ for location eval_f_bb6_in_v1

Found invariant X₅ ≤ X₀ ∧ X₁ ≤ X₁₄ for location eval_f_bb3_in

Found invariant X₅ ≤ X₀ ∧ 5 ≤ X₃ ∧ 6 ≤ X₃+X₁₁ ∧ 4+X₁₁ ≤ X₃ ∧ X₁ ≤ X₁₄ ∧ 1 ≤ X₁₁ for location eval_f_bb5_in_v1

Found invariant X₅ ≤ X₀ ∧ X₁₁ ≤ X₃ ∧ X₁ ≤ X₁₄ for location eval_f_stop

All Bounds

Timebounds

Overall timebound:inf {Infinity}
t₅₄: 1 {O(1)}
t₅₅: 1 {O(1)}
t₅₆: 1 {O(1)}
t₅₉: X₁₄+1 {O(n)}
t₆₀: X₁₄+1 {O(n)}
t₆₁: 1 {O(1)}
t₆₃: X₁₄+2 {O(n)}
t₆₄: X₁₄+2 {O(n)}
t₆₅: X₁₄+2 {O(n)}
t₆₆: X₁₄+2 {O(n)}
t₆₈: X₁₄+1 {O(n)}
t₆₉: 1 {O(1)}
t₇₀: 1 {O(1)}
t₇₁: 1 {O(1)}
t₇₂: X₁₄+1 {O(n)}
t₇₃: inf {Infinity}
t₇₄: 1 {O(1)}
t₇₅: 1 {O(1)}
t₇₆: inf {Infinity}
t₇₇: 1 {O(1)}
t₇₈: 1 {O(1)}
t₁₄₅: X₁₄+2 {O(n)}
t₁₄₆: X₁₄+2 {O(n)}
t₁₄₇: X₁₄+2 {O(n)}
t₁₄₈: X₁₄+2 {O(n)}
t₁₄₉: X₁₄+2 {O(n)}
t₁₅₀: X₁₄+2 {O(n)}
t₁₅₁: X₁₄+2 {O(n)}
t₁₅₂: X₁₄+2 {O(n)}
t₁₅₃: 21⋅X₁₄+46 {O(n)}
t₁₅₄: 5⋅X₁₄+14 {O(n)}
t₁₅₅: 13⋅X₁₄+30 {O(n)}
t₁₅₆: 12⋅X₁₄+28 {O(n)}
t₁₅₇: 19⋅X₁₄+41 {O(n)}
t₁₅₈: 94⋅X₁₄+210 {O(n)}
t₁₅₉: 36⋅X₁₄+84 {O(n)}

Costbounds

Overall costbound: inf {Infinity}
t₅₄: 1 {O(1)}
t₅₅: 1 {O(1)}
t₅₆: 1 {O(1)}
t₅₉: X₁₄+1 {O(n)}
t₆₀: X₁₄+1 {O(n)}
t₆₁: 1 {O(1)}
t₆₃: X₁₄+2 {O(n)}
t₆₄: X₁₄+2 {O(n)}
t₆₅: X₁₄+2 {O(n)}
t₆₆: X₁₄+2 {O(n)}
t₆₈: X₁₄+1 {O(n)}
t₆₉: 1 {O(1)}
t₇₀: 1 {O(1)}
t₇₁: 1 {O(1)}
t₇₂: X₁₄+1 {O(n)}
t₇₃: inf {Infinity}
t₇₄: 1 {O(1)}
t₇₅: 1 {O(1)}
t₇₆: inf {Infinity}
t₇₇: 1 {O(1)}
t₇₈: 1 {O(1)}
t₁₄₅: X₁₄+2 {O(n)}
t₁₄₆: X₁₄+2 {O(n)}
t₁₄₇: X₁₄+2 {O(n)}
t₁₄₈: X₁₄+2 {O(n)}
t₁₄₉: X₁₄+2 {O(n)}
t₁₅₀: X₁₄+2 {O(n)}
t₁₅₁: X₁₄+2 {O(n)}
t₁₅₂: X₁₄+2 {O(n)}
t₁₅₃: 21⋅X₁₄+46 {O(n)}
t₁₅₄: 5⋅X₁₄+14 {O(n)}
t₁₅₅: 13⋅X₁₄+30 {O(n)}
t₁₅₆: 12⋅X₁₄+28 {O(n)}
t₁₅₇: 19⋅X₁₄+41 {O(n)}
t₁₅₈: 94⋅X₁₄+210 {O(n)}
t₁₅₉: 36⋅X₁₄+84 {O(n)}

Sizebounds

t₅₄, X₀: X₀ {O(n)}
t₅₄, X₁: X₁ {O(n)}
t₅₄, X₂: X₂ {O(n)}
t₅₄, X₃: X₃ {O(n)}
t₅₄, X₄: X₄ {O(n)}
t₅₄, X₆: X₆ {O(n)}
t₅₄, X₇: X₇ {O(n)}
t₅₄, X₈: X₈ {O(n)}
t₅₄, X₉: X₉ {O(n)}
t₅₄, X₁₀: X₁₀ {O(n)}
t₅₄, X₁₁: X₁₁ {O(n)}
t₅₄, X₁₂: X₁₂ {O(n)}
t₅₄, X₁₃: X₁₃ {O(n)}
t₅₄, X₁₄: X₁₄ {O(n)}
t₅₅, X₀: X₀ {O(n)}
t₅₅, X₁: X₁ {O(n)}
t₅₅, X₂: X₂ {O(n)}
t₅₅, X₃: X₃ {O(n)}
t₅₅, X₄: X₄ {O(n)}
t₅₅, X₇: X₇ {O(n)}
t₅₅, X₈: X₈ {O(n)}
t₅₅, X₉: X₉ {O(n)}
t₅₅, X₁₀: X₁₀ {O(n)}
t₅₅, X₁₁: X₁₁ {O(n)}
t₅₅, X₁₂: X₁₂ {O(n)}
t₅₅, X₁₃: X₁₃ {O(n)}
t₅₅, X₁₄: X₁₄ {O(n)}
t₅₆, X₁: X₁₄ {O(n)}
t₅₆, X₃: X₃ {O(n)}
t₅₆, X₄: X₄ {O(n)}
t₅₆, X₇: X₇ {O(n)}
t₅₆, X₈: X₈ {O(n)}
t₅₆, X₉: X₉ {O(n)}
t₅₆, X₁₀: X₁₀ {O(n)}
t₅₆, X₁₁: X₁₁ {O(n)}
t₅₆, X₁₂: X₁₂ {O(n)}
t₅₆, X₁₃: X₁₃ {O(n)}
t₅₆, X₁₄: X₁₄ {O(n)}
t₅₉, X₁: X₁₄ {O(n)}
t₅₉, X₂: 1 {O(1)}
t₅₉, X₃: X₃ {O(n)}
t₅₉, X₄: X₄ {O(n)}
t₅₉, X₈: X₈+4 {O(n)}
t₅₉, X₁₀: X₁₄ {O(n)}
t₅₉, X₁₁: X₁₁ {O(n)}
t₅₉, X₁₂: X₁₂ {O(n)}
t₅₉, X₁₃: X₁₃ {O(n)}
t₅₉, X₁₄: X₁₄ {O(n)}
t₆₀, X₁: X₁₄ {O(n)}
t₆₀, X₃: X₃ {O(n)}
t₆₀, X₄: X₄ {O(n)}
t₆₀, X₈: X₈+4 {O(n)}
t₆₀, X₁₀: X₁₄ {O(n)}
t₆₀, X₁₁: X₁₁ {O(n)}
t₆₀, X₁₂: X₁₂ {O(n)}
t₆₀, X₁₃: X₁₃ {O(n)}
t₆₀, X₁₄: X₁₄ {O(n)}
t₆₁, X₀: X₀ {O(n)}
t₆₁, X₁: X₁ {O(n)}
t₆₁, X₂: X₂ {O(n)}
t₆₁, X₃: X₃ {O(n)}
t₆₁, X₄: X₄ {O(n)}
t₆₁, X₅: X₅ {O(n)}
t₆₁, X₆: X₆ {O(n)}
t₆₁, X₇: X₇ {O(n)}
t₆₁, X₈: X₈ {O(n)}
t₆₁, X₉: X₉ {O(n)}
t₆₁, X₁₀: X₁₀ {O(n)}
t₆₁, X₁₁: X₁₁ {O(n)}
t₆₁, X₁₂: X₁₂ {O(n)}
t₆₁, X₁₃: X₁₃ {O(n)}
t₆₁, X₁₄: X₁₄ {O(n)}
t₆₃, X₁: X₁₄ {O(n)}
t₆₃, X₃: X₃ {O(n)}
t₆₃, X₄: X₄ {O(n)}
t₆₃, X₈: X₈+4 {O(n)}
t₆₃, X₁₀: X₁₀+X₁₄ {O(n)}
t₆₃, X₁₁: X₁₁ {O(n)}
t₆₃, X₁₂: X₁₂ {O(n)}
t₆₃, X₁₃: X₁₃ {O(n)}
t₆₃, X₁₄: X₁₄ {O(n)}
t₆₄, X₁: X₁₄ {O(n)}
t₆₄, X₃: X₃ {O(n)}
t₆₄, X₄: X₄ {O(n)}
t₆₄, X₈: X₈+4 {O(n)}
t₆₄, X₁₀: X₁₀+X₁₄ {O(n)}
t₆₄, X₁₁: X₁₁ {O(n)}
t₆₄, X₁₂: X₁₂ {O(n)}
t₆₄, X₁₃: X₁₃ {O(n)}
t₆₄, X₁₄: X₁₄ {O(n)}
t₆₅, X₁: X₁₄ {O(n)}
t₆₅, X₃: X₃ {O(n)}
t₆₅, X₄: X₄ {O(n)}
t₆₅, X₈: X₈+4 {O(n)}
t₆₅, X₁₀: X₁₀+X₁₄ {O(n)}
t₆₅, X₁₁: X₁₁ {O(n)}
t₆₅, X₁₂: X₁₂ {O(n)}
t₆₅, X₁₃: X₁₃ {O(n)}
t₆₅, X₁₄: X₁₄ {O(n)}
t₆₆, X₁: X₁₄ {O(n)}
t₆₆, X₃: X₃ {O(n)}
t₆₆, X₄: X₄ {O(n)}
t₆₆, X₈: X₈+4 {O(n)}
t₆₆, X₁₀: X₁₀+X₁₄ {O(n)}
t₆₆, X₁₁: X₁₁ {O(n)}
t₆₆, X₁₂: X₁₂ {O(n)}
t₆₆, X₁₃: X₁₃ {O(n)}
t₆₆, X₁₄: X₁₄ {O(n)}
t₆₈, X₁: X₁₄ {O(n)}
t₆₈, X₂: 1 {O(1)}
t₆₈, X₃: X₃ {O(n)}
t₆₈, X₄: X₄ {O(n)}
t₆₈, X₈: X₈+4 {O(n)}
t₆₈, X₁₀: 7⋅X₁₀+7⋅X₁₄ {O(n)}
t₆₈, X₁₁: X₁₁ {O(n)}
t₆₈, X₁₂: X₁₂ {O(n)}
t₆₈, X₁₃: X₁₃ {O(n)}
t₆₈, X₁₄: X₁₄ {O(n)}
t₆₉, X₁: 4⋅X₁₄ {O(n)}
t₆₉, X₃: 4⋅X₁₁ {O(n)}
t₆₉, X₄: 4⋅X₁₂ {O(n)}
t₆₉, X₈: 4⋅X₈+16 {O(n)}
t₆₉, X₁₀: 7⋅X₁₀+7⋅X₁₄ {O(n)}
t₆₉, X₁₁: 4⋅X₁₁ {O(n)}
t₆₉, X₁₂: 4⋅X₁₂ {O(n)}
t₆₉, X₁₃: 4⋅X₁₃ {O(n)}
t₆₉, X₁₄: 4⋅X₁₄ {O(n)}
t₇₀, X₁: 3⋅X₁₄ {O(n)}
t₇₀, X₃: 3⋅X₁₁ {O(n)}
t₇₀, X₄: 3⋅X₁₂ {O(n)}
t₇₀, X₈: 3⋅X₈+12 {O(n)}
t₇₀, X₁₀: 5⋅X₁₀+5⋅X₁₄ {O(n)}
t₇₀, X₁₁: 3⋅X₁₁ {O(n)}
t₇₀, X₁₂: 3⋅X₁₂ {O(n)}
t₇₀, X₁₃: 3⋅X₁₃ {O(n)}
t₇₀, X₁₄: 3⋅X₁₄ {O(n)}
t₇₁, X₁: 3⋅X₁₄ {O(n)}
t₇₁, X₃: 3⋅X₁₁ {O(n)}
t₇₁, X₄: 3⋅X₁₂ {O(n)}
t₇₁, X₈: 3⋅X₈+12 {O(n)}
t₇₁, X₁₀: 5⋅X₁₀+5⋅X₁₄ {O(n)}
t₇₁, X₁₁: 3⋅X₁₁ {O(n)}
t₇₁, X₁₂: 3⋅X₁₂ {O(n)}
t₇₁, X₁₃: 3⋅X₁₃ {O(n)}
t₇₁, X₁₄: 3⋅X₁₄ {O(n)}
t₇₂, X₁: X₁₄ {O(n)}
t₇₂, X₂: 1 {O(1)}
t₇₂, X₃: X₃ {O(n)}
t₇₂, X₄: X₄ {O(n)}
t₇₂, X₈: X₈+4 {O(n)}
t₇₂, X₁₀: X₁₄ {O(n)}
t₇₂, X₁₁: X₁₁ {O(n)}
t₇₂, X₁₂: X₁₂ {O(n)}
t₇₂, X₁₃: X₁₃ {O(n)}
t₇₂, X₁₄: X₁₄ {O(n)}
t₇₃, X₁: 10⋅X₁₄ {O(n)}
t₇₃, X₈: 10⋅X₈+40 {O(n)}
t₇₃, X₁₀: 17⋅X₁₀+17⋅X₁₄ {O(n)}
t₇₃, X₁₁: 10⋅X₁₁ {O(n)}
t₇₃, X₁₂: 10⋅X₁₂ {O(n)}
t₇₃, X₁₃: 10⋅X₁₃ {O(n)}
t₇₃, X₁₄: 10⋅X₁₄ {O(n)}
t₇₄, X₁: 20⋅X₁₄ {O(n)}
t₇₄, X₈: 20⋅X₈+80 {O(n)}
t₇₄, X₁₀: 34⋅X₁₀+34⋅X₁₄ {O(n)}
t₇₄, X₁₁: 20⋅X₁₁ {O(n)}
t₇₄, X₁₂: 20⋅X₁₂ {O(n)}
t₇₄, X₁₃: 20⋅X₁₃ {O(n)}
t₇₄, X₁₄: 20⋅X₁₄ {O(n)}
t₇₅, X₁: 20⋅X₁₄ {O(n)}
t₇₅, X₈: 20⋅X₈+80 {O(n)}
t₇₅, X₁₀: 34⋅X₁₀+34⋅X₁₄ {O(n)}
t₇₅, X₁₁: 20⋅X₁₁ {O(n)}
t₇₅, X₁₂: 20⋅X₁₂ {O(n)}
t₇₅, X₁₃: 20⋅X₁₃ {O(n)}
t₇₅, X₁₄: 20⋅X₁₄ {O(n)}
t₇₆, X₁: 10⋅X₁₄ {O(n)}
t₇₆, X₈: 10⋅X₈+40 {O(n)}
t₇₆, X₁₀: 17⋅X₁₀+17⋅X₁₄ {O(n)}
t₇₆, X₁₁: 10⋅X₁₁ {O(n)}
t₇₆, X₁₂: 10⋅X₁₂ {O(n)}
t₇₆, X₁₃: 10⋅X₁₃ {O(n)}
t₇₆, X₁₄: 10⋅X₁₄ {O(n)}
t₇₇, X₁: 40⋅X₁₄ {O(n)}
t₇₇, X₈: 40⋅X₈+160 {O(n)}
t₇₇, X₁₀: 68⋅X₁₀+68⋅X₁₄ {O(n)}
t₇₇, X₁₁: 40⋅X₁₁ {O(n)}
t₇₇, X₁₂: 40⋅X₁₂ {O(n)}
t₇₇, X₁₃: 40⋅X₁₃ {O(n)}
t₇₇, X₁₄: 40⋅X₁₄ {O(n)}
t₇₈, X₀: X₀ {O(n)}
t₇₈, X₁: X₁ {O(n)}
t₇₈, X₂: X₂ {O(n)}
t₇₈, X₃: X₃ {O(n)}
t₇₈, X₄: X₄ {O(n)}
t₇₈, X₅: X₅ {O(n)}
t₇₈, X₆: X₆ {O(n)}
t₇₈, X₇: X₇ {O(n)}
t₇₈, X₈: X₈ {O(n)}
t₇₈, X₉: X₉ {O(n)}
t₇₈, X₁₀: X₁₀ {O(n)}
t₇₈, X₁₁: X₁₁ {O(n)}
t₇₈, X₁₂: X₁₂ {O(n)}
t₇₈, X₁₃: X₁₃ {O(n)}
t₇₈, X₁₄: X₁₄ {O(n)}
t₁₄₅, X₁: X₁₄ {O(n)}
t₁₄₅, X₃: X₃ {O(n)}
t₁₄₅, X₄: X₄ {O(n)}
t₁₄₅, X₈: X₈+12 {O(n)}
t₁₄₅, X₁₀: X₁₀+X₁₄ {O(n)}
t₁₄₅, X₁₁: X₁₁ {O(n)}
t₁₄₅, X₁₂: X₁₂ {O(n)}
t₁₄₅, X₁₃: X₁₃ {O(n)}
t₁₄₅, X₁₄: X₁₄ {O(n)}
t₁₄₆, X₁: X₁₄ {O(n)}
t₁₄₆, X₃: X₃ {O(n)}
t₁₄₆, X₄: X₄ {O(n)}
t₁₄₆, X₈: X₈+12 {O(n)}
t₁₄₆, X₁₀: X₁₀+X₁₄ {O(n)}
t₁₄₆, X₁₁: X₁₁ {O(n)}
t₁₄₆, X₁₂: X₁₂ {O(n)}
t₁₄₆, X₁₃: X₁₃ {O(n)}
t₁₄₆, X₁₄: X₁₄ {O(n)}
t₁₄₇, X₁: X₁₄ {O(n)}
t₁₄₇, X₃: X₃ {O(n)}
t₁₄₇, X₄: X₄ {O(n)}
t₁₄₇, X₈: X₈+12 {O(n)}
t₁₄₇, X₁₀: X₁₀+X₁₄ {O(n)}
t₁₄₇, X₁₁: X₁₁ {O(n)}
t₁₄₇, X₁₂: X₁₂ {O(n)}
t₁₄₇, X₁₃: X₁₃ {O(n)}
t₁₄₇, X₁₄: X₁₄ {O(n)}
t₁₄₈, X₁: X₁₄ {O(n)}
t₁₄₈, X₃: X₃ {O(n)}
t₁₄₈, X₄: X₄ {O(n)}
t₁₄₈, X₈: X₈+12 {O(n)}
t₁₄₈, X₁₀: X₁₀+X₁₄ {O(n)}
t₁₄₈, X₁₁: X₁₁ {O(n)}
t₁₄₈, X₁₂: X₁₂ {O(n)}
t₁₄₈, X₁₃: X₁₃ {O(n)}
t₁₄₈, X₁₄: X₁₄ {O(n)}
t₁₄₉, X₀: 3 {O(1)}
t₁₄₉, X₁: X₁₄ {O(n)}
t₁₄₉, X₂: 0 {O(1)}
t₁₄₉, X₃: X₃ {O(n)}
t₁₄₉, X₄: X₄ {O(n)}
t₁₄₉, X₈: 2⋅X₈+4 {O(n)}
t₁₄₉, X₁₀: X₁₀+X₁₄ {O(n)}
t₁₄₉, X₁₁: X₁₁ {O(n)}
t₁₄₉, X₁₂: X₁₂ {O(n)}
t₁₄₉, X₁₃: X₁₃ {O(n)}
t₁₄₉, X₁₄: X₁₄ {O(n)}
t₁₅₀, X₀: 3 {O(1)}
t₁₅₀, X₁: X₁₄ {O(n)}
t₁₅₀, X₂: 0 {O(1)}
t₁₅₀, X₃: X₃ {O(n)}
t₁₅₀, X₄: X₄ {O(n)}
t₁₅₀, X₈: 4 {O(1)}
t₁₅₀, X₁₀: X₁₀+X₁₄ {O(n)}
t₁₅₀, X₁₁: X₁₁ {O(n)}
t₁₅₀, X₁₂: X₁₂ {O(n)}
t₁₅₀, X₁₃: X₁₃ {O(n)}
t₁₅₀, X₁₄: X₁₄ {O(n)}
t₁₅₁, X₀: 3 {O(1)}
t₁₅₁, X₁: X₁₄ {O(n)}
t₁₅₁, X₂: 0 {O(1)}
t₁₅₁, X₃: X₃ {O(n)}
t₁₅₁, X₄: X₄ {O(n)}
t₁₅₁, X₈: 4 {O(1)}
t₁₅₁, X₁₀: X₁₀+X₁₄ {O(n)}
t₁₅₁, X₁₁: X₁₁ {O(n)}
t₁₅₁, X₁₂: X₁₂ {O(n)}
t₁₅₁, X₁₃: X₁₃ {O(n)}
t₁₅₁, X₁₄: X₁₄ {O(n)}
t₁₅₂, X₀: 4 {O(1)}
t₁₅₂, X₁: X₁₄ {O(n)}
t₁₅₂, X₃: X₃ {O(n)}
t₁₅₂, X₄: X₄ {O(n)}
t₁₅₂, X₈: 4 {O(1)}
t₁₅₂, X₁₀: X₁₀+X₁₄ {O(n)}
t₁₅₂, X₁₁: X₁₁ {O(n)}
t₁₅₂, X₁₂: X₁₂ {O(n)}
t₁₅₂, X₁₃: X₁₃ {O(n)}
t₁₅₂, X₁₄: X₁₄ {O(n)}
t₁₅₃, X₀: 4 {O(1)}
t₁₅₃, X₁: X₁₄ {O(n)}
t₁₅₃, X₃: X₃ {O(n)}
t₁₅₃, X₄: X₄ {O(n)}
t₁₅₃, X₈: 4 {O(1)}
t₁₅₃, X₁₀: 2⋅X₁₀+2⋅X₁₄ {O(n)}
t₁₅₃, X₁₁: X₁₁ {O(n)}
t₁₅₃, X₁₂: X₁₂ {O(n)}
t₁₅₃, X₁₃: X₁₃ {O(n)}
t₁₅₃, X₁₄: X₁₄ {O(n)}
t₁₅₄, X₀: 4 {O(1)}
t₁₅₄, X₁: X₁₄ {O(n)}
t₁₅₄, X₃: X₃ {O(n)}
t₁₅₄, X₄: X₄ {O(n)}
t₁₅₄, X₈: 4 {O(1)}
t₁₅₄, X₁₀: 2⋅X₁₀+2⋅X₁₄ {O(n)}
t₁₅₄, X₁₁: X₁₁ {O(n)}
t₁₅₄, X₁₂: X₁₂ {O(n)}
t₁₅₄, X₁₃: X₁₃ {O(n)}
t₁₅₄, X₁₄: X₁₄ {O(n)}
t₁₅₅, X₀: 4 {O(1)}
t₁₅₅, X₁: X₁₄ {O(n)}
t₁₅₅, X₃: X₃ {O(n)}
t₁₅₅, X₄: X₄ {O(n)}
t₁₅₅, X₈: 4 {O(1)}
t₁₅₅, X₁₀: 2⋅X₁₀+2⋅X₁₄ {O(n)}
t₁₅₅, X₁₁: X₁₁ {O(n)}
t₁₅₅, X₁₂: X₁₂ {O(n)}
t₁₅₅, X₁₃: X₁₃ {O(n)}
t₁₅₅, X₁₄: X₁₄ {O(n)}
t₁₅₆, X₀: 3 {O(1)}
t₁₅₆, X₁: X₁₄ {O(n)}
t₁₅₆, X₂: 0 {O(1)}
t₁₅₆, X₃: X₃ {O(n)}
t₁₅₆, X₄: X₄ {O(n)}
t₁₅₆, X₈: 3 {O(1)}
t₁₅₆, X₉: 0 {O(1)}
t₁₅₆, X₁₀: X₁₀+X₁₄ {O(n)}
t₁₅₆, X₁₁: X₁₁ {O(n)}
t₁₅₆, X₁₂: X₁₂ {O(n)}
t₁₅₆, X₁₃: X₁₃ {O(n)}
t₁₅₆, X₁₄: X₁₄ {O(n)}
t₁₅₇, X₀: 3 {O(1)}
t₁₅₇, X₁: X₁₄ {O(n)}
t₁₅₇, X₂: 0 {O(1)}
t₁₅₇, X₃: X₃ {O(n)}
t₁₅₇, X₄: X₄ {O(n)}
t₁₅₇, X₈: 4 {O(1)}
t₁₅₇, X₉: 0 {O(1)}
t₁₅₇, X₁₀: X₁₀+X₁₄ {O(n)}
t₁₅₇, X₁₁: X₁₁ {O(n)}
t₁₅₇, X₁₂: X₁₂ {O(n)}
t₁₅₇, X₁₃: X₁₃ {O(n)}
t₁₅₇, X₁₄: X₁₄ {O(n)}
t₁₅₈, X₀: 3 {O(1)}
t₁₅₈, X₁: X₁₄ {O(n)}
t₁₅₈, X₂: 0 {O(1)}
t₁₅₈, X₃: X₃ {O(n)}
t₁₅₈, X₄: X₄ {O(n)}
t₁₅₈, X₈: 4 {O(1)}
t₁₅₈, X₁₀: X₁₀+X₁₄ {O(n)}
t₁₅₈, X₁₁: X₁₁ {O(n)}
t₁₅₈, X₁₂: X₁₂ {O(n)}
t₁₅₈, X₁₃: X₁₃ {O(n)}
t₁₅₈, X₁₄: X₁₄ {O(n)}
t₁₅₉, X₀: 4 {O(1)}
t₁₅₉, X₁: X₁₄ {O(n)}
t₁₅₉, X₃: X₃ {O(n)}
t₁₅₉, X₄: X₄ {O(n)}
t₁₅₉, X₈: 4 {O(1)}
t₁₅₉, X₁₀: X₁₀+X₁₄ {O(n)}
t₁₅₉, X₁₁: X₁₁ {O(n)}
t₁₅₉, X₁₂: X₁₂ {O(n)}
t₁₅₉, X₁₃: X₁₃ {O(n)}
t₁₅₉, X₁₄: X₁₄ {O(n)}